Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to graph these curves?

  1. Nov 16, 2004 #1

    I was wondering how would I graph a sketch of these curves without knowing any values of them? They are orthogonal trajectories btw

    i) x^2 + y^2 = ax
    x^2 + y^2 = by

    ii) y = ax^3
    x^2 + 3y^2 = b

    Thanks in advnace.
  2. jcsd
  3. Nov 17, 2004 #2


    User Avatar
    Science Advisor

    x2+ y2= ax is the same as

    x2- ax+ y2= 0. Now complete the square in the x variable:

    x2- ax+ a2/4+ y2= a2/4
    (x- a/2)2+ y2= a2/2.

    That's a circle with center at (a/2, 0) and radius a/2 (so it goes through (0,0)).

    x2 + y2 = by

    Same thing: a circle with center at (0, b/2) and radius b/2 (and goes through (0,0)).

    y = ax3
    Well, that's just a pretty standard cubic. Goes through(-2,-8a), (-1, -a), (0,0), (1, a), (2, 8a), etc.

    x2 + 3y2 = b
    Same as x2/b + y2/(b/3)= 1,
    an ellipse with center at (0,0) vertices (√(b), 0), (-&radic(b),0), (0, √(b/3)), (0,-√(b/3)).
  4. Nov 17, 2004 #3
    Thanks a lot man. Really appreciate it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook